/// @file
/// @author David Pilger <dpilger26@gmail.com>
/// [GitHub Repository](https://github.com/dpilger26/NumCpp)
///
/// License
/// Copyright 2018-2021 David Pilger
///
/// Permission is hereby granted, free of charge, to any person obtaining a copy of this
/// software and associated documentation files(the "Software"), to deal in the Software
/// without restriction, including without limitation the rights to use, copy, modify,
/// merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
/// permit persons to whom the Software is furnished to do so, subject to the following
/// conditions :
///
/// The above copyright notice and this permission notice shall be included in all copies
/// or substantial portions of the Software.
///
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
/// INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
/// PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE
/// FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
/// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
/// DEALINGS IN THE SOFTWARE.
///
/// Description
/// Special Functions
///
#pragma once

#include "NumCpp/Core/Types.hpp"
#include "NumCpp/NdArray.hpp"
#include "NumCpp/Special/factorial.hpp"

#ifndef NO_USE_BOOST
#include "boost/math/special_functions/factorials.hpp"
#endif

namespace nc
{
    namespace special
    {
        //============================================================================
        // Method Description:
        /// Returns the number of permutaions of n choose r. P(n, r)
        ///
        /// @param  n: the total number of items
        /// @param  r: the number of items taken
        /// @return
        ///				double
        ///
        inline double pnr(uint32 n, uint32 r)
        {
            if (r > n)
            {
                return 0.0;
            }
            else if (r == n)
            {
                return factorial(n);
            }

            double combinations = 1.0;

#ifndef NO_USE_BOOST
            if (n <= boost::math::max_factorial<double>::value)
            {
                const double nFactorial = factorial(n);
                const double nMinusRFactoral = factorial(n - r);

                combinations = nFactorial / nMinusRFactoral;
            }
            else
            {
#endif
                const uint32 lower = n - r + 1;
                combinations = static_cast<double>(lower);
                for (uint32 i = lower + 1; i <= n; ++i)
                {
                    combinations *= static_cast<double>(i);
                }
#ifndef NO_USE_BOOST
            }
#endif

            return combinations;
        }
    }  // namespace special
} // namespace nc
